HAMPTON, Ga. — Sen. Marco Rubio’s brawling with Republican presidential front-runner Donald Trump won over some NASCAR dads, a sizable bloc in Southern states voting Super Tuesday that will be key for him to close the gap with the real estate mogul.

Race fans at the Atlanta Motor Speedway for Sunday’s Folds of Honor QuikTrip 500 said they were swayed by Mr. Rubio’s newfound moxie or have fresh doubts about Mr. Trump after the two viciously clashed in the Republican presidential debate last week and kept trading jabs ever since.

“He went head to head with Trump. He stood up to him, and he knocked Trump down,” said Eric Penney, 37, a commercial real estate agent in Georgia who showed up on race day shirtless and wearing an American flag as a cape.

He planned to cast his vote on Super Tuesday, when 11 states hold primaries or caucuses with hundreds of delegates up for grabs.

Mr. Penney had been a Trump fan but had growing reservations about the billionaire businessman and reality TV star’s suitability for the Oval Office. He was leaning toward retired neurosurgeon Ben Carson until Mr. Rubio’s strong debate performance.

“That’s when I decided to swing my vote to Rubio,” he said, adding that the senator from Florida is more electable and has a better shot at defeating Democratic front-runner Hillary Clinton. “We just got to get Trump out of the pole position.”

NASCAR dads were first identified as a political force in the 2004 race, when Democrats attempted to reconnect with white working-class Southern men.

This year, those voters are courted almost exclusively by Republican candidates, with Mr. Trump expected to capture the lion’s share in the primaries.

In the debate last week, Mr. Rubio dinged Mr. Trump for using illegal immigrant labor to build one of his skyscrapers and challenged the billionaire businessman’s depth on health care and foreign policy, including accusing him of taking anti-Israel positions.

Since then, the two have exchanged a series of barbs about their personal grooming habits and character. Mr. Rubio hurled the charge of “con man,” and Mr. Trump responded with the epithet “choke artist.”

The big question for Mr. Rubio is whether he waited too long to aggressively challenge Mr. Trump, who won three of the first four contests and continues to hold big leads in most states voting on Super Tuesday and beyond.

Bud Miller, who came to the race with a group of friends including Mr. Penny, said he was leaning toward Mr. Trump but worried about his foreign policy chops, one of Mr. Rubio’s strengths.

“That’s a huge thing for me. I’ve got a lot of people in the military,” said Mr. Miller, 33, a heavy equipment operator for a waste disposal company.

He also voiced concerns about Mr. Trump’s temperament for dealing with foreign leaders. “You can’t just be pissing people off,” he said.

Phil Gwarjanki, 55, who owns the Buster Miles Ford dealership in Heflin, Alabama, another Super Tuesday state, said he favored Mr. Trump until the debate.

“That’s what made me do a big question mark,” he said. “Rubio swayed me a little bit. He stood up to the billionaire. He didn’t back off of him. It made an impression.”

Still, Mr. Trump retained a deep reservoir of support at the NASCAR track.

“Rubio sucks,” said Robert Hardin, 56, a die-hard Trump supporter who owns a furniture retail business in Indiana, which holds its primary May 3.

Mr. Hardin noted that Mr. Rubio was among the Senate’s bipartisan “Gang of Eight,” which pushed a comprehensive immigration reform bill that critics derided as amnesty. He said Mr. Rubio had the same immigration stance as President Obama.

“There’s too many illegal workers,” said Mr. Hardin, a lifelong Democrat who never before voted for a Republican for president but was switching sides to vote for Mr. Trump.